Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 11?
- How many black squares will there be in Figure 47?
- Which figure is made up of 1932 black squares?
(a)
Pattern for the number of black squares
Figure
1: 1 x
5 = 1 x (
1 +
4) = 5
Figure
2: 2 x
6 = 2 x (
2 +
4) = 12
Figure
3: 3 x
7 = 3 x (
3 +
4) = 21
Formula
Number of black squares = Figure Number x (Figure Number + 4)
Number of black squares for Figure 11
= 11 x (11 + 4)
= 11 x 15
= 165
(b)
Number of black squares in Figure 47
= 47 x (47 + 4)
= 47 x 51
= 2397
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 42
42 x 46 = 1932 (✔)
42 x (42 + 4) = 1932
Figure Number with 1932 black squares = 42
Answer(s): (a) 165; (b) 2397; (c) 42